From a sample of 50 predominantly inactive galaxies with direct supermassive black hole mass measurements, it has recently been established that barred galaxies tend to reside rightward of the M bh-σ relation defined by nonbarred galaxies. Either black holes in barred galaxies tend to be anemic or the central velocity dispersions in these galaxies have a tendency to be elevated by the presence of the bar. The latter option is in accord with studies connecting larger velocity dispersions in galaxies with old bars, while the former scenario is at odds with the observation that barred galaxies do not deviate from the M bh-luminosity relation. Using a sample of 88 galaxies with active galactic nuclei, whose supermassive black hole masses have been estimated from their associated emission lines, we reveal for the first time that they also display this same general behavior in the M bh-σ diagram depending on the presence of a bar or not. A new symmetrical and nonsymmetrical "barless" M bh-σ relation is derived using 82 nonbarred galaxies. The barred galaxies are shown to reside on or up to ∼1 dex below this relation. This may explain why narrow-line Seyfert 1 galaxies appear offset from the "barless" M bh-σ relation, and has far-reaching implications given that over half of the disk galaxy population are barred.